The linsolve function does not check assumptions like integer=True. The solve function does but only as a final check. Neither of these really solves integer systems in the way that you would want here.
The diophantine function is for integer equations but does not handle systems of equations so is also not what you want. I put some code that illustrates improvements to diophantine in this issue: https://github.com/sympy/sympy/issues/20682 Using that code you have: In [9]: diop_new(eqnList, [h, l, m, n]) Out[9]: ∅ In [11]: diop_new([eqnList[0]], [h, l, m, n]) Out[11]: {((t₁, 2⋅t₀, t₂, t₀), (t₀, t₁, t₂), (ℤ, ℤ, ℤ))} In [13]: diop_new([eqnList[1]], [h, l, m, n]) Out[13]: {((t₀, 2⋅t₀ + 4⋅t₁ + 3, t₀ + t₁, t₂), (t₀, t₁, t₂), (ℤ, ℤ, ℤ))} That code is not well tested but you might find it useful. -- Oscar On Mon, 4 Aug 2025 at 15:06, Steve Collins <steve.collin...@gmail.com> wrote: > > Apologies if this is obvious, but I'm having trouble using solve to find out > if solutions exist or not (I don't really care what they are, just whether or > not there are any), for simultaneous equations with integer variables. > > For the following example, which has no solutions, solve returns [] (no > solution), or a solution, depending on the order of the symbols given. That > is, it sometimes works but sometimes fails to realize that there is no > solution. > > For comparison, Mathematica seems to be correct, i.e. Reduce[l == 2 n && 2 h > + l - 4 m - 3 == 0, {h, l, n, m}, Integers] correctly returns 'False'. Sympy > linsolve, on the other hand, never gives a null result, so it seems to do > worse than solve. > > > Example Python code below. Any advice would be gratefully appreciated! > > from sympy import * > > (h, l, m, n) = symbols(['h', 'l', 'm', 'n'], integer = True) > > # these equations should have no solution as l must be both odd and even > eqnList = [Eq(l, 2*n), Eq(2*h + l - 4*m - 3, 0)] > > # however, some orderings of the symbols to solve over fail to give no > solution (empty list) > print(solve(eqnList, [l, n, h, m] )) # returns [] - correct > print(solve(eqnList, [h, m, n, l] )) # returns {h: -l/2 + 2*m + 3/2, n: l/2} > - should give [] ? > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/sympy/0c23f1e5-15e8-4345-a961-f8be9728e127n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sympy/CAHVvXxQUDXi35eVxjvkU%3DGxJ6i1chW8YHNAyKymv7v10-LzGBQ%40mail.gmail.com.
